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Structured Hidden Markov Models


  • Jan Bulla

    (Georg-August-University Goettingen)

  • Ingo Bulla

    (Université de Bretagne-Occidentale)


The lion’s share of hidden Markov models (HMMs) /Markov regime switching models considered in economic research incorporates a comparably small number of states. The popularity of models with mostly two or three states principally results from their good interpretability: often regime changes can be linked to abrupt external events. A further reason lies in the number of parameters of the transition probability matrix (TPM) having a growth rate which is quadratic in the number of states. Thus, the estimation procedures quickly become unstable and strongly dependent on the choice of the initial values due to overparametrization. From the intuitive point of view it is at least discussible whether, e.g., macroeconomic or political changes are not anticipated. If this is the case, HMMs with comparably smooth transition between many states constitute an attractive alternative. We present structured hidden Markov model (SHMMs). The SHMM approach reduces the number of parameters significantly by providing the TPM with a distinct architecture. We compare the performance of SHMMs with common HMMs in the context of return series. Moreover, we present an implementation of the estimation procedures via the freely available software package R

Suggested Citation

  • Jan Bulla & Ingo Bulla, 2006. "Structured Hidden Markov Models," Computing in Economics and Finance 2006 437, Society for Computational Economics.
  • Handle: RePEc:sce:scecfa:437

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    More about this item


    Hidden Markov model; Number of States; Structured Hidden Markov Model; Return Series; Overparameterization;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques


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